the internet is full of answers to your question. On unix like machines, google for keyword. ssh-keygen, running that command for example as : ssh-keygen -t rsa on server 1 will give you two files id_rsa and id_rsa.pub. You save id_rsa into your $HOME/.ssh and you copy id_rsa.pub to server2:$HOME/.ssh/authorized_keys. Make sure the permission are 0600.